On non-normal numbers

Bodo Volkmann

Compositio Mathematica (1964)

  • Volume: 16, page 186-190
  • ISSN: 0010-437X

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Volkmann, Bodo. "On non-normal numbers." Compositio Mathematica 16 (1964): 186-190. <http://eudml.org/doc/88892>.

@article{Volkmann1964,
author = {Volkmann, Bodo},
journal = {Compositio Mathematica},
keywords = {number theory},
language = {eng},
pages = {186-190},
publisher = {Kraus Reprint},
title = {On non-normal numbers},
url = {http://eudml.org/doc/88892},
volume = {16},
year = {1964},
}

TY - JOUR
AU - Volkmann, Bodo
TI - On non-normal numbers
JO - Compositio Mathematica
PY - 1964
PB - Kraus Reprint
VL - 16
SP - 186
EP - 190
LA - eng
KW - number theory
UR - http://eudml.org/doc/88892
ER -

References

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  1. Besicovitch, A.S. [1] On the sum of digits of real numbers represented in the dyadic number system. Math. Ann.110, 321-330 (1934). Zbl0009.39503MR1512941JFM60.0949.01
  2. Borel, E. [2] Les probabilités dénombrables et leurs applications arithmétiques. Rend. Circ. Mat. Palermo27, 247-271 (1909). Zbl40.0283.01JFM40.0283.01
  3. Cassels, J.W.S. [3] On a problem of Steinhaus, Colloq. Math.7 (1959), 95-101. Zbl0090.26004MR113863
  4. Eggleston, H.G. [4] The fractional dimension of a set defined by decimal properties. Quart. J. Math.20, 31-36 (1949). Zbl0031.20801MR31026
  5. Eggleston, H.G. [5] Sets of fractional dimensions which occur in some problems of number theory. Proc. London Math. Soc.54, 42-93 (1951). Zbl0045.16603MR48504
  6. Hausdorff, F. [6] Dimension und äusseres Mass. Math. Ann.79, 157-179 (1918). Zbl46.0292.01MR1511917JFM46.0292.01
  7. Knichal, V. [7] Dyadische Entwicklungen und Hausdorffsches Mass. Mém. Soc. Roy. Sci. Bohême, Cl. des Sciences, 1933, Nr. 14, 1-18. Zbl0009.20401
  8. Schmidt, W. [8] On normal numbers, Pac. Journ. Math.10, 661-672 (1960). Zbl0093.05401MR117212
  9. Volkmann, B. [9] Über Hausdorffsche Dimensionen von Mengen, die durch Zifferneigenschaften charakterisiert sind. III. Math. Z.59, 279-290 (1953). Zbl0051.29701MR59338
  10. Volkmann, B. [10] IV. Math. Z.59, 425-433 (1954). Zbl0055.05103MR60570
  11. [11] V. Math. Z.65, 389-413 (1956). Zbl0071.05303MR92813
  12. [12] VI. Math. Z.68, 439-449 (1958). Zbl0079.07903MR100578
  13. Wall, D.D. [13] Normal Numbers. Ph. D. Thesis, 1949, University of California, Berkeley, California. 

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